Multivariable low-pressure exhaust gas recirculation control

ABSTRACT

Methods and systems are provided for adjusting a LP-EGR valve and an LP intake throttle to provide a desired LP-EGR flow rate while maintaining a minimum differential pressure. In one example, a method for a turbocharged engine method comprises: responsive to a differential between intake and exhaust pressure below a threshold, adjusting a LP-EGR valve while adjusting a LP intake throttle to regulate a LP-EGR flow rate and the differential to respective setpoints; and responsive to the differential above the threshold, saturating the LP-EGR valve to minimize the differential while actuating the throttle to regulate the flow rate to its setpoint. In this way, control of the LP-EGR system may be more robust to disturbances at very low differential pressures, require less actuator movement, and increase fuel economy.

BACKGROUND AND SUMMARY

Engine systems may utilize recirculation of exhaust gas from an engineexhaust system to an engine intake system, a process referred to asexhaust gas recirculation (EGR), to reduce regulated emissions. Forexample, a turbocharged engine system may include a low-pressure (LP)EGR system which recirculates exhaust gas from the exhaust system to theintake passage upstream of a turbocharger compressor. Accordingly,exhaust gas may be recirculated into a low-pressure air induction systemupstream of the compressor, resulting in a compressed mixture of freshintake air and EGR downstream of the compressor. An EGR valve may becontrolled to achieve a desired intake air dilution, the desired intakeair dilution based on engine operating conditions.

However, due to the small differential pressures inherent to LP-EGRloops, turbocharged engine systems may also include a LP intake throttleto increase the differential pressure such that higher EGR rates can beachieved. There are competing requirements that constrain the degree ofthrottling. On one hand, excessive throttling unnecessarily increasesfuel consumption. On the other hand, too little throttling can cause thesystem to operate at particularly low differential pressures, whichnecessitates high control gains and thereby reduces the control systemrobustness to disturbances.

The inventors herein have recognized the above issue and have devisedvarious approaches to address it. In particular, systems and methods forcontrolling an LP intake throttle and an LP-EGR valve are disclosed. Inone example, a turbocharged engine method, comprises: responsive to adifferential between intake and exhaust pressure below a threshold,adjusting a LP-EGR valve while adjusting a LP intake throttle toregulate a LP-EGR flow rate and the differential to respectivesetpoints; and responsive to the differential above the threshold,saturating the LP-EGR valve to minimize the differential while actuatingthe throttle to regulate the flow rate to its setpoint. In this way,control of the LP-EGR system may be more robust, require less actuatormovement, and increase fuel economy.

In another example, a turbocharged engine method, comprises: responsiveto a differential between intake and exhaust pressure below a threshold,adjusting a LP-EGR valve while adjusting a LP intake throttle toregulate a LP-EGR flow rate and the differential respectively to a flowsetpoint and a differential setpoint; and responsive to the differentialabove the threshold, in a first mode saturating the LP-EGR valve tominimize the differential while actuating the throttle to regulate theflow rate to the flow setpoint, and in a second mode, saturating theintake throttle to minimize the differential while actuating the LP-EGRvalve to regulate the flow rate to the flow setpoint. In this way, thecontrol system may be more robust to disturbances at very lowdifferential pressures and fuel consumption due to excessive throttlingmay be decreased.

In another example, an internal combustion engine system comprises: aturbocharger including a compressor connected to a turbine, thecompressor in communication with an intake manifold of the engine andthe turbine in communication with an exhaust manifold of the engine; alow-pressure (LP) exhaust gas recirculation (EGR) passage including anEGR valve and an intake throttle connecting the intake manifold and theexhaust manifold, said EGR valve responsive to an EGR valve controlsignal and said intake throttle responsive to an intake throttle controlsignal for regulating a flow rate into said intake manifold and adifferential pressure in said LP-EGR passage; a controller configuredwith instructions stored in non-transitory memory that when executed,cause the controller to: generate a flow rate error based upon areference flow rate and a measured flow rate; generate a differentialpressure error based upon a reference differential pressure and ameasured differential pressure; calculate a minimum and a maximumachievable flow rates; apply the minimum and the maximum achievable flowrates as anti-windup limits to a first proportional-integral controller;execute the first proportional-integral controller to generate anadjusted flow rate setpoint responsive to the flow rate error; calculatea minimum and a maximum achievable differential pressures responsive tothe adjusted flow rate setpoint; apply the minimum and the maximumachievable differential pressures as anti-windup limits to a secondproportional-integral controller; execute the secondproportional-integral controller to generate an adjusted differentialpressure setpoint responsive to the differential pressure error; executea linearization controller to generate an EGR valve actuator positionand a LP intake throttle actuator position responsive to the adjustedflow rate setpoint and the adjusted differential pressure setpoint; andactuate the EGR valve to the EGR valve actuator position and the LPintake throttle to the LP intake throttle actuator position. In thisway, control of the LP-EGR valve and the LP intake throttle canautomatically switch between a multivariable control mode that improvesrobustness at very low differential pressures and a chained-actuatorcontrol mode that minimizes fuel consumption.

The above advantages and other advantages, and features of the presentdescription will be readily apparent from the following DetailedDescription when taken alone or in connection with the accompanyingdrawings.

It should be understood that the summary above is provided to introducein simplified form a selection of concepts that are further described inthe detailed description. It is not meant to identify key or essentialfeatures of the claimed subject matter, the scope of which is defineduniquely by the claims that follow the detailed description.Furthermore, the claimed subject matter is not limited toimplementations that solve any disadvantages noted above or in any partof this disclosure.

BRIEF DESCRIPTIONS OF THE DRAWINGS

FIG. 1 shows a schematic depiction of an engine and an associatedexhaust gas recirculation system.

FIG. 2 shows a high-level flow chart illustrating a routine that may beimplemented for performing LP-EGR valve and LP intake throttleadjustments responsive to the output of a differential pressure sensor.

FIG. 3 shows a block diagram illustrating an example approach for LP-EGRcontrol.

FIG. 4 shows a high-level flow chart illustrating a routine that may beimplemented for performing LP-EGR valve and LP intake throttleadjustments responsive to a LP-EGR flow rate setpoint.

FIG. 5 shows a set of graphs illustrates a limitation strategy for fourpossible cases of a single-actuator saturation.

FIG. 6 shows a set of graphs illustrating a set of achievable LP-EGRvalve positions and throttle positions and a corresponding set ofachievable LP-EGR flow rates and differential pressures.

FIG. 7 shows a set of graphs illustrating a demonstration of a LP-EGRcontroller functioning as a multivariable controller.

FIG. 8 shows a set of graphs illustrating a demonstration of a LP-EGRcontroller functioning as a chained-actuator controller.

DETAILED DESCRIPTION

The following description relates to a system and method for controllinglow-pressure exhaust gas recirculation mass flow rate and differentialpressure using a low-pressure exhaust gas recirculation valve and alow-pressure throttle. As shown in FIG. 1, a boosted engine may beconfigured with a low-pressure (LP) exhaust gas recirculation (EGR)system that may include an LP-EGR valve for adjusting an amount ofexhaust gas recirculated to the engine intake as well as an LP intakethrottle for adjusting the differential pressure across the LP-EGRvalve. As shown in FIG. 2, control of the LP-EGR valve and the LP intakethrottle may include a multivariable mode and a chained-actuator modedepending on the differential pressure across the LP-EGR valve. As shownin FIG. 3, a controller enabling two such control modes may include acontroller designed by input-output linearization in addition to twoouter proportional-integral (PI) control loops. A limitation strategyfor the PI controllers may include using the minimum and maximumachievable EGR flow rates and differential pressures as anti-winduplimits, as shown in FIG. 4. This limitation strategy ensures that if oneactuator saturates, the unsaturated actuator will prioritize trackingthe EGR flow rate over the differential pressure, as shown in FIG. 5.The minimum and maximum achievable flow rates and differential pressuresare constrained by the actuation ability of the system, as shown in FIG.6. A demonstration that the disclosed system and methods exhibit amultivariable mode and a chained-actuator mode is shown in FIGS. 7 and8.

FIG. 1 shows a schematic depiction of a vehicle system 6. The vehiclesystem 6 includes an engine system 8, including engine 10 coupled toemission control system 22. Engine 10 includes a plurality of cylinders30. Engine 10 also includes an intake 23 and an exhaust 25. Intake 23may receive fresh air from the atmosphere through intake passage 42.Intake passage 42 may include a first air intake throttle 82 configuredto adjust the amount of fresh air that is received through intakepassage 42. Intake 23 may further include a second main intake throttle62 fluidly coupled to the engine intake manifold 44 via intake passage42. Second intake throttle 62 may be positioned downstream of firstintake throttle 82, and may be configured to adjust the flow of anintake gas stream entering engine intake manifold 44. Exhaust 25includes an exhaust manifold 48 leading to an exhaust passage 45 thatroutes exhaust gas to the atmosphere via tailpipe 35.

Engine 10 may be a boosted engine including a boosting device, such asturbocharger 50. Turbocharger 50 may include a compressor 52, arrangedalong intake passage 42, and a turbine 54, arranged along exhaustpassage 45. The amount of boost provided by the turbocharger may bevaried by an engine controller. An optional charge after-cooler 84 maybe included downstream of compressor 52 in the intake passage to reducethe temperature of the intake air compressed by the turbocharger.Specifically, after-cooler 84 may be included downstream of first intakethrottle 82 and upstream of second intake throttle 62.

Emission control system 22, coupled to exhaust passage 45, may includeone or more emission control devices 70 mounted in a close-coupledposition in the exhaust. One or more emission control devices mayinclude a particulate filter, SCR catalyst, three-way catalyst, lean NOxtrap, oxidation catalyst, etc. The emission control devices may bepositioned downstream of turbine 54 and upstream and/or downstream ofLP-EGR path 73 in exhaust passage 45. Engine 10 may further include oneor more exhaust gas recirculation (EGR) passages for recirculating atleast a portion of exhaust gas from exhaust passage 45 to intake passage42. For example, the engine may include a low-pressure EGR (LP-EGR)system 72 with an LP-EGR passage 73 coupling the engine exhaust,downstream of turbine 54, to the engine intake, upstream of compressor52. LP-EGR system 72 may be operated during conditions such as in thepresence of turbocharger boost and/or when exhaust gas temperature isabove a threshold. An EGR valve 39, positioned in LP-EGR passage 73upstream of the compressor, may be configured to adjust an amount and/orrate of exhaust gas diverted through the EGR passage. LP-EGR passage 73may further include an LP-EGR cooler 74 to lower the temperature ofexhaust gas being recirculated into the engine intake. In thisconfiguration, the EGR passage may be configured to provide low pressureEGR, and EGR valve 39 may be a LP-EGR valve. Further, first intake valve82 may be referred to as a low-pressure (LP) intake throttle. Inalternate embodiments, a high-pressure EGR (HP-EGR) system (not shown)may also be included wherein a HP-EGR passage may be configured todivert at least some exhaust gas from the engine exhaust, upstream ofthe turbine, to the engine intake, downstream of the compressor.

In some embodiments, one or more sensors may be positioned within LP-EGRpassage 73 to provide an indication of one or more of a pressure,temperature, and air-fuel ratio of exhaust gas recirculated through theLP-EGR passage. For example, sensors 75 and 76 may be pressure sensorslocated upstream and downstream of LP-EGR valve 39. Exhaust gas divertedthrough LP-EGR passage 73 may be diluted with fresh intake air at mixingpoint 90, located at the junction of LP-EGR passage 73 and intakepassage 42. Specifically, by adjusting EGR valve 39 in coordination withLP intake throttle 82 (positioned in the air intake passage of theengine intake, upstream of the compressor), a dilution of the EGR flowmay be adjusted.

Engine 10 may be controlled at least partially by a control system 14including controller 12 and by input from a vehicle operator via aninput device (not shown). Control system 14 is configured to receiveinformation from a plurality of sensors 16 (various examples of whichare described herein) and sending control signals to a plurality ofactuators 81. As one example, sensors 16 may include exhaust gas sensor126 coupled to exhaust manifold 48, an exhaust temperature sensor 128and exhaust pressure sensor 129 located downstream of the emissioncontrol device 70 in tailpipe 35, oxygen sensor 92 coupled upstream ofmain intake throttle 62, and various sensors in LP-EGR passage 73, suchas pressure sensors 75 and 76 located upstream and downstream of theLP-EGR valve 39 and an EGR flow rate sensor 77. Various exhaust gassensors may also be included in exhaust passage 45 downstream ofemission control device 70, such as particulate matter (PM) sensors, NOxsensors, oxygen sensors, ammonia sensors, hydrocarbon sensors, etc.Other sensors such as additional pressure, temperature, air/fuel ratioand composition sensors may be coupled to various locations in thevehicle system 6. As another example, actuators 81 may include fuelinjector 66, EGR valve 39, LP intake throttle 82, and main intakethrottle 62. Other actuators, such as a variety of additional valves andthrottles, may be coupled to various locations in vehicle system 6.Controller 12 may receive input data from the various sensors, processthe input data, and trigger the actuators in response to the processedinput data based on instruction or code programmed therein correspondingto one or more routines. For example, controller 12 may be configured tocompute a differential pressure across the LP-EGR valve 39 bycalculating the difference between input data received from pressuresensor 76 and pressure sensor 75. An example control routine isdescribed herein with regard to FIG. 2.

FIG. 2 shows a high-level flow chart for an example method 200 forcontrolling a LP-EGR system in accordance with the current disclosure.In particular, method 200 relates to using two different controlstrategies responsive to a differential pressure across the LP-EGR valve39. Method 200 will be described herein with reference to the componentsand systems depicted in FIG. 1, though it should be understood that themethod may be applied to other systems without departing from the scopeof this disclosure. Method 200 may be carried out by controller 12, andmay be stored as executable instructions in non-transitory memory.

Method 200 may begin at 205. At 205, method 200 may include evaluatingoperating conditions. Operating conditions may include, but are notlimited to, LP-EGR differential pressure, LP-EGR flow rate, LP-EGR valveposition, LP intake throttle position, etc. Evaluating operatingconditions may comprise receiving input data from various sensors andperforming a computation using said input data. For example, the LP-EGRdifferential pressure across the LP-EGR valve 39 may be calculated bycomputing the difference between pressure data from pressure sensors 75and 76. In the absence of pressure sensors 75 and 76, the LP-EGRdifferential pressure may be approximated from a pre-compressor gaugepressure measurement, e.g., Δp_(lpEgrMeas)≈p_(amb)−p_(cmprUs), whichneglects the minor pressure drop across the exhaust tailpipe.

Continuing at 210, the differential pressure Δp_(lpEgrMeas) across theLP-EGR valve 39 is compared to a LP-EGR differential pressure setpointΔp_(setpoint). The LP-EGR differential pressure setpoint Δp_(setpoint)may be set to a low yet non-zero differential pressure, for example, 5hectopascal (hPa). If the differential pressure Δp_(lpEgrMeas) isgreater than the differential setpoint Δp_(setpoint), method 200 maycontinue to 215. At 215, the controller 12 may act as a chained-actuatorcontroller. The controller 12 closes the LP intake throttle 82 tominimize the differential pressure, and then adjusts the LP-EGR valve 39to regulate the LP-EGR flow rate to a LP-EGR flow rate setpointW_(lpEgr). This control strategy minimizes the fuel consumption due toLP-EGR pumping work. Method 200 may then end. Otherwise, if thedifferential pressure Δp_(lpEgrMeas) is less than the differentialsetpoint Δp_(setpoint), method 200 may continue to 220.

At 220, method 200 may act as a multivariable controller. The controller12 simultaneously adjusts the LP-EGR valve 39 and the LP intake throttle82 to regulate LP-EGR flow rate W_(lpEgr) and differential pressureΔp_(lpEgrMeas) to their respective setpoints. This control strategyallows the system to avoid large control gains and reduced controlsystem robustness that occur at very low differential pressures. Method200 may then end.

The control method 200 thus uses two control strategies responsive tothe differential pressure with respect to the differential pressuresetpoint. Using method 200, the controller 12 may automatically switchbetween functioning as a chained-actuator controller and a multivariablecontroller, each with its own advantages. An example approach toimplementing method 200 is disclosed herein with regard to FIGS. 3 and4.

FIG. 3 shows an example approach 300 for LP-EGR control. Exampleapproach 300 is designed with an input-output linearization andproportional-integral control. Example approach 300 includes asteady-state virtual plant 320 and two outer loops with PI controllers312 and 314.

Reference signal r₁=W_(lpEgrDes) 305 represents a reference desiredLP-EGR flow rate, while reference signal r₂=Δp_(lpEgrDes) 307 representsa reference desired LP-EGR differential pressure. Feedback signaly₁=W_(lpEgrMeas) 341 represents the measured LP-EGR flow rate, whilefeedback signal y₂=Δp_(lpEgrMeas) 343 represents the measured LP-EGRdifferential pressure. Junction 306 computes the difference betweenreference signal 305 and feedback signal 341; this difference is theerror associated with the LP-EGR flow rate. Junction 308 computes thedifference between reference signal 307 and feedback signal 343; thisdifference is the error associated with the LP-EGR differentialpressure.

Example approach 300 may include an outer loop PI controller 312 and anouter loop PI controller 314. Outer loop PI controller 312 generates anadjusted input v₁=W_(lpEgrDes) including a proportional gain term and anintegral gain term for the error r₁−y₁ computed at junction 306. Outerloop PI controller 314 similarly generates an adjusted inputv₂=Δp_(lpEgrDes) including a proportional gain term and an integral gainterm for the error r₂−y₂ computed at junction 308. Outer loop PIcontrollers 312 and 314 provide zero steady-state tracking error andimprove robustness to modeling errors in an inverse plant model Ψ(v,w),discussed further herein. PI controllers 312 and 314 may be calibratedto yield a closed-loop time constant of approximately 150-200 ms forboth loops.

Virtual plant 320 features a controller 324 and a plant model 327.Controller 324 uses the inputs v₁ and v₂ representing desired LP-EGRflow rate and LP-EGR differential pressure to determine the appropriateLP-EGR valve throttle position u₁=θ_(lpEgrVlvDes) and LP intake throttleposition u₂=θ_(lpIntThrDes). Plant model 327 represents the physicalLP-EGR system, and therefore is based on incompressible-flow orificeequations for the LP-intake throttle, LP-EGR path, and tailpipe, and theassociated dynamics are attributed to sensors and actuators. Thedynamics of Plant 327 are non-linear and multivariable:

{dot over (x)}=f(x,w)+Bu,

y=Cx,

and so an appropriate control law Ψ(x,v,w) must be chosen to linearizeand decouple the plant. However, the plant dynamics are fast relative tothe time scale of the outer loops, with time constants of approximately50 ms or less. Therefore, the high-bandwidth nature of the plant allowsan assumption that the plant is always at steady-state, therebyeliminating a virtual feedback x, as shown by virtual plant 320. Withthis assumption, an input-output linearization of the virtual plant 320is reduced to finding an algebraic inversion of the multivariablenon-linear plant model. In the preferred embodiment, a unique solutionrepresenting controller 324 is given by:

${u = {{\Psi \; \left( {v,\; w} \right)} = \begin{bmatrix}{\; {\alpha_{\; {lpEgr}}^{- 1}\left\lbrack \mspace{11mu} \frac{\; v_{\; 1}}{\; \sqrt{2\; v_{\; 2}\; w_{\; 2}}} \right\rbrack}} \\{\; {\alpha_{\; {ais}}^{- 1}\left\lbrack \frac{\; {A_{\; {tp}}\; \left( \; {w_{\; 1}\mspace{11mu} - \mspace{11mu} v_{\; 1}} \right)}}{\; \sqrt{{2\; v_{\; 2}\; w_{\; 2}\; A_{\; {tp}}^{\; 2}}\mspace{11mu} - \mspace{11mu} \left( \; {w_{\; 1}\mspace{11mu} - \mspace{11mu} v_{\; 1}\mspace{11mu} + \mspace{11mu} w_{\; 3}} \right)}} \right\rbrack}}\end{bmatrix}}},$

where A_(tp) is the tailpipe area, α_(lpEgr) is the actuatorposition-to-area transfer function giving the effective area of theLP-EGR path A_(lpEgr) (including LP-EGR passage 73, valve 39, and cooler74), and α_(ais) is the actuator position-to-area transfer functiongiving the effective area of the air intake system A_(ais) (including LPintake throttle 82). Note that the control inputs u, exogenous inputs w,and outputs y, are formally defined as:

${u:=\begin{pmatrix}\theta_{lpEgrVlvDes} \\\theta_{lpIntThrDes}\end{pmatrix}},{w:=\begin{pmatrix}W_{cmpr} \\\rho_{amb} \\W_{f}\end{pmatrix}},{y:=\begin{pmatrix}W_{lpEgrMeas} \\{\Delta \; p_{lpEgrMeas}}\end{pmatrix}},$

where W_(cmpr) is the mass flow rate through the compressor, ρ_(amb) isthe density of ambient air, and W_(f) is the mass flow rate of injectedfuel.

In the preferred embodiment, the steady-state plant model 327 is modeledusing a collection of incompressible-flow orifice equations and massbalances. Plant model 327 may be written simply as:

y=h(u,w)=[h ₁(u,w)h ₂(u,w)]^(T),

where the functions h₁(u, w) and h₂(u, w) are given by:

h ₁(u,w)=f ₁[α_(lpEgr)(u ₁),α_(ais)(u ₂),A _(tp) ,w ₁ ,w ₃],

h ₂(u,w)=f ₂[α_(lpEgr)(u ₁),α_(ais)(u ₂),A _(tp) ,w ₁ ,w ₂ ,w ₃].

Functions ƒ₁ and ƒ₂ may be obtained by solving a collection of threeorifice equations and two mass conservation constraints. The threeorifice equations used to model the gas flow through the LP-EGR passage73, air-intake system 42, and tailpipe 35 are given by:

W _(lpEgr) =A _(lpEgr)√{square root over (2Δp _(lpEgr)ρ_(amb),)}

W _(ais) =A _(ais)√{square root over (2Δp _(ais)ρ_(amb),)}

W _(tp) =A _(tp)√{square root over (2Δp _(tp)ρ_(amb),)}

where the differential pressures are given by:

Δp _(lpEgr) =p _(lpEgrUs) −p _(cmprUs),

Δp _(ais) =p _(amb) −p _(cmprUs),

Δp _(tp) =p _(lpEgrUs) −p _(amb).

Pressure p_(lpEgrUs) refers to a pressure measured upstream of LP-EGRvalve 39 while pressure p_(cmprUs) refers to a pressure measuredupstream of compressor 52. Mass conservation is enforced at the LP-EGRmixing point 90 and for the total mass entering the air path through theair-intake system 42 and exiting the air path through the tailpipe 35:

W _(cmpr) =W _(lpEgr) +W _(ais),

W _(tp) =W _(ais) +W _(f).

Solving the above set of orifice flow and mass conservation equationsfor the LP-EGR flow rate W_(lpEgr) and the LP-EGR differential pressureΔp_(lpEgr) yields:

${W_{lpEgr} = {{f_{1}\left( {A_{lpEgr},A_{ais},A_{tp},W_{cmpr},W_{f}} \right)} = \frac{\begin{matrix}{{A_{lpEgr}^{2}{A_{ais}^{2}\left( {W_{cmpr} + W_{f}} \right)}} + {A_{lpEgr}^{2}A_{tp}^{2}W_{cmpr}} -} \\{A_{lpEgr}A_{ais}A_{tp}\sqrt{{A_{ais}^{2}\left( {W_{cmpr} + W_{f}} \right)}^{2} + {A_{tp}^{2}W_{f}^{2}} - {A_{lpEgr}^{2}W_{f}^{2}}}}\end{matrix}}{{A_{lpEgr}^{2}A_{ais}^{2}} + {A_{lpEgr}^{2}A_{tp}^{2}} - {A_{ais}^{2}A_{tp}^{2}}}}},{{\Delta \; p_{lpEgr}} = {{f_{2}\left( {A_{lpEgr},A_{ais},A_{tp},W_{cmpr},W_{f}} \right)} = \left\{ {\begin{matrix}{{\left( {\frac{W_{cmpr}^{2}}{A_{ais}^{2}} + \frac{\left( {W_{cmpr} + W_{f}} \right)^{2}}{A_{tp}^{2}}} \right)\frac{1}{2\rho_{amb}}},} & {{A_{lpEgr} = 0},} \\{\frac{{f_{1}\left( {A_{lpEgr},A_{ais},A_{tp},W_{cmpr},W_{f}} \right)}^{2}}{2\rho_{amb}A_{lpEgr}^{2}},} & {A_{lpEgr} > 0}\end{matrix}.} \right.}}$

Those skilled in the art will appreciate that the multivariable staticplant model 327 just described accurately models the behavior of theLP-EGR system. Furthermore, the linearized controller Ψ(v, w) isspecifically obtained from plant model 327 by determining an inversefunction of y=h(u, w) that maps y to u, given w, such that virtual plant320 is linearized and decoupled:

y=h(u,w)=h(Ψ(v,w),w)=v.

Example approach 300 for LP-EGR control exhibits two distinctive controlbehaviors, described herein with regard to FIG. 2 and further describedherein and with regard to FIGS. 5, 6, 7, and 8.

FIG. 4 shows a high-level flow chart illustrating an example controlmethod 400 implemented by the controller described herein with regard toFIG. 3. In particular, method 400 comprises a PI control limitationstrategy that prioritizes tracking the LP-EGR flow rate setpoint. Thatis, if either the LP-EGR valve or the LP intake throttle saturates, thenthe ability to simultaneously track the LP-EGR flow rate setpoint andthe differential pressure setpoint is lost and priority is given totracking the flow rate setpoint.

Method 400 may begin at 405. At 405, method 400 may include evaluatingoperating conditions. Evaluating operating conditions may includemeasuring the control inputs u, exogenous inputs w, and outputs y, asdefined herein and with regard to FIG. 3. Method 400 may then continueto 410.

At 410, method 400 may include calculating minimum and maximumachievable LP-EGR flow rates. Calculating minimum and maximum achievableLP-EGR flow rates v₁ ^(max)(k) and v₂ ^(max)(k) may include evaluating,for example:

v ₁ ^(max)(k)=h ₁([u ₁ ^(max) u ₂ ^(max)]^(T) ,w(k)),

v ₁ ^(min)(k)=h ₁([u ₁ ^(min) u ₂ ^(min)]_(T) ,w(k)),

where k is the current time step. Example results of such a calculationare further discussed herein and with regard to FIG. 6. Method 400 maythen continue to 415.

At 415, method 400 may include applying the minimum and maximum flowrates v₁ ^(max)(k) and v₂ ^(max)(k) as anti-windup limits on PIcontroller 312. Applying minimum and maximum flow rates as anti-winduplimits on PI controller 312 restrains a subsequent PI commanded flowrate v₁* to the physically achievable LP-EGR flow rates, that is:

v ₁ ^(min)(k)≦v ₁ *≦v ₁ ^(max).

Method 400 may then continue to 420. At 420, method 400 may includeexecuting the flow rate PI controller 312 to generate a commanded flowrate v₁*. Method 400 may then continue to 425.

At 425, method 400 may include calculating minimum and maximumachievable differential pressures Δp constrained to achieve thecommanded flow rate. Calculating minimum and maximum achievabledifferential pressures v₂ ^(min)(k) and v₂ ^(max)(k) may includeevaluating, for example:

${{v_{2}^{m\; {ax}}(k)} = {\max\limits_{u \in S_{u}}\left\{ {\left. {h_{2}\left( {u,{w(k)}} \right)} \middle| {h_{1}\left( {u,{w(k)}} \right)} \right. = {v_{1}^{*}(k)}} \right\}}},{{v_{2}^{m\; i\; n}(k)} = {\min\limits_{u \in S_{u}}\left\{ {\left. {h_{2}\left( {u,{w(k)}} \right)} \middle| {h_{1}\left( {u,{w(k)}} \right)} \right. = {v_{1}^{*}(k)}} \right\}}},$

where S_(u) is the domain wherein the actuator positions areconstrained,

S _(u)={(u ₁ ,u ₂)|u ₁ ^(min) ≦u ₁ ≦u ₁ ^(max) ,u ₂ ^(min) ≦u ₂ ≦u ₂^(max)}.

In this way, the minimum and maximum achievable LP-EGR differentialpressures are subject to the constraint of achieving the commandedLP-EGR flow rate v₁(k)=v₁*. Example results of such a calculation arefurther discussed herein and with regard to FIG. 6. Method 400 may thencontinue to 430.

At 430, method 400 may include applying the minimum and maximumachievable differential pressures Δp as anti-windup limits on PIcontroller 314. Applying the minimum and maximum achievable differentialpressures as anti-windup limits on PI controller 314 restrains asubsequent PI commanded differential pressure v₂* to the physicallyachievable differential pressures, that is:

v ₂ ^(min)(k)≦v ₂ *≦v ₂ ^(max)(k).

Method 400 may then continue to 435. At 435, method 400 may includeexecuting the differential pressure PI controller to generate acommanded differential pressure v₂*. Method 400 may then continue to440.

At 440, method 400 may include executing a linearization to generatecommanded actuator positions. Executing a linearization to generatecommanded actuator positions may be carried out by controller 324 inaccordance with the linearization scheme disclosed with regard to FIG.3, such that:

${{u(k)} = {\Psi \left( {{v^{*}(k)},{w(k)}} \right)}};{{v^{*}(k)}:={\begin{pmatrix}v_{1}^{*} \\v_{2}^{*}\end{pmatrix}.}}$

Method 400 may then continue to 445. At 445, method 400 may includecommanding the actuators to the generated commanded actuator positions.The generated commanded actuator positions are given by u(k). Method 400may then continue to 450. At 450, method 400 may include incrementingthe timer by one step, for example, k=k+1. Method 400 may then end.

FIG. 5 shows a set of graphs 500 illustrating a limitation strategy forall four possible cases of single-actuator saturation in accordance withthe current disclosure. Graph 510 shows a plot of the LP-EGR flow rateW_(lpEgr) over time. The dashed line in graph 510 represents the LP-EGRflow rate setpoint, and the solid line represents the measured LP-EGRflow rate. Graph 520 shows a plot of the LP-EGR differential pressureΔp_(lpEgr) over time. The dashed line in graph 520 represents the LP-EGRdifferential pressure setpoint, and the solid line represents themeasured LP-EGR differential pressure. Graph 530 shows a plot of the LPintake throttle θ_(lpIntThr) over time. Graph 540 shows a plot of theLP-EGR valve position θ_(lpEgrVlv) over time.

From 0 seconds to 5 seconds, the LP intake throttle and the LP-EGR valveare both partially open, as shown in graphs 530 and 540. The measuredLP-EGR flow rate and LP-EGR differential pressure are both close totheir respective setpoints, as seen in graphs 510 and 520.

From 5 seconds to 10 seconds, the LP intake throttle actuator issaturated, as seen in graph 530. The LP intake throttle positionθ_(lpIntThr) is at 0%, meaning that the LP intake throttle is fullyopen. In response to the LP intake throttle actuator saturation, theLP-EGR valve position increases as seen in graph 540. Graph 510 showsthat during this time period, the measured LP-EGR flow rate ismaintained near the setpoint. Meanwhile, graph 520 shows that themeasured LP-EGR differential pressure Δp_(lpEgr) is unable to reach thedifferential pressure setpoint.

From 10 seconds to 15 seconds, the LP intake throttle actuator is againsaturated. However, in this case the LP intake throttle positionθ_(lpIntThr) is at 100%, meaning that the LP intake throttle is fullyclosed. In response to the LP intake throttle actuator saturation, theLP-EGR valve position θ_(lpEgrVlv) increases. This increased LP-EGRvalve position θ_(lpEgrVlv) maintains the measured LP-EGR flow rateW_(lpEgr) very close to the flow rate setpoint. Meanwhile, the measuredLP-EGR differential pressure Δp_(lpEgr) is once again unable to reachthe differential pressure setpoint.

From 15 seconds to 20 seconds, the LP-EGR valve actuator is saturated.The LP-EGR valve position θ_(lpEgrVlv) is at 100%, meaning that theLP-EGR valve is fully open. In response to the LP-EGR valve actuatorsaturation, the LP intake throttle position θ_(lpIntThr) slightlydecreases. This decreased LP intake throttle position θ_(lpIntThr)maintains the measured LP-EGR flow rate W_(lpEgr) very close to the flowrate setpoint. Meanwhile, the measured LP-EGR differential pressureΔp_(lpEgr) is unable to reach the differential pressure setpoint.

From 20 seconds to 25 seconds, the LP-EGR valve actuator is againsaturated. The LP-EGR flow rate W_(lpEgr) is zero so the LP-EGR valveposition θ_(lpEgrVlv) is at 0%, that is, the LP-EGR valve is fullyclosed to trivially achieve the flow rate setpoint. The LP intakethrottle position θ_(lpIntThr) decreases in order to maintain themeasured LP-EGR differential pressure Δp_(lpEgr) at the differentialpressure setpoint. This is the only case where an actuator is saturatedwhile both setpoints are achieved.

In each case, the LP-EGR mass flow rate setpoint is tracked with zerosteady-state error while a control error is present in the LP-EGRdifferential pressure. In the last case, the LP-EGR valve is fullyclosed while the LP intake throttle is partially open. This only occurswhen the desired LP-EGR flow rate W_(lpEgrDes)=0 and the desired LP-EGRdifferential pressure Δp_(lpEgrDes) is set larger than the unthrottleddifferential pressure, causing throttling while the LP-EGR valve isclosed. This case is not useful during normal engine operation, and canbe avoided by setting Δp_(lpEgrDes)=0 whenever W_(lpEgrDes)=0, therebyforcing the throttle fully open whenever the desired flow rate is zero.In this way, the multivariable controller can be forced to operate as achained-actuator controller by intentionally setting the differentialpressure setpoint unachievably low, for example Δp_(lpEgrDes)=0. In thepreferred embodiment, the differential pressure setpoint Δp_(lpEgrDes)=5hPa so that the controller operates as a chained-actuator controllerwhen the differential pressure is above the setpoint, and resumesoperation as a multivariable controller when the differential pressureis below the setpoint.

FIG. 6 shows an illustration of the set of achievable LP-EGR valve andthrottle positions and corresponding LP-EGR flow rates and differentialpressures in accordance with the current disclosure. The plots shownwere created using the system and methods disclosed above with regard toFIGS. 3 and 4, assuming a compressor flow rate W_(cmpr)=400 kg/h anddensity of ambient air ρ_(amb)=1.19 kg/m³.

Graph 610 shows the set of achievable LP-EGR valve positions u₁ and LPintake throttle positions u₂. The x-axis of graph 610 represents theLP-EGR valve position u₁ as an actuation percentage, where 0%corresponds to a fully closed valve and 100% corresponds to a fullyopened valve. The y-axis of graph 610 represents the LP intake throttleposition u₂ as an actuation percentage, where 0% corresponds to a fullyopen throttle and 100% corresponds to a fully closed throttle. Theconventions are established by setting 0% to the un-energized actuatorposition, which for a diesel implementation, is open for the LP intakethrottle and closed for the LP-EGR valve. Dashed line 612 encloses thefull set of possible LP-EGR valve and throttle positions. Since theLP-EGR valve and the LP intake throttle are both able to change fromfully closed to fully open, dashed line 612 encloses the entireconfiguration space. Dashed line 612 has four corners denoted by points620, 622, 624, and 626. Point 620 corresponds to a fully closed LPintake throttle and a fully closed LP-EGR valve. Point 622 correspondsto a fully closed LP intake throttle and a fully open LP-EGR valve.Point 624 corresponds to a fully open LP intake throttle and a fullyclosed LP-EGR valve. Point 626 corresponds to a fully open LP intakethrottle and a fully open LP-EGR valve.

Graph 630 shows the set of achievable LP-EGR flow rates v₁ and LP-EGRdifferential pressures v₂. The x-axis of graph 630 represents the LP-EGRflow rate in units of kilograms per hour. The y-axis of graph 630represents the LP-EGR differential pressure in units of hectopascals.Dashed line 632 encloses the full set of possible LP-EGR flow rates anddifferential pressures achievable by the present invention. Dashed line632 has four corners denoted by points 640, 642, 644, and 646. Eachcorner of dashed line 632 corresponds to a corner of dashed line 612 ingraph 610. For example, point 640 corresponds to point 620, meaning thatwhen the LP-intake throttle is fully closed and the LP-EGR valve isfully closed, the LP-EGR flow rate v₁=0 kg/h and the LP-EGR flow ratev₂≈70 hPa. Similarly, point 642 corresponds to the actuator positionsgiven by point 622, point 644 corresponds to the actuator positionsgiven by point 624, and point 646 corresponds to the actuator positionsgiven by point 626.

Since the PI limitation strategy disclosed herein and with regard toFIG. 4 prioritizes tracking the LP-EGR flow rate over the LP-EGRdifferential pressure, it is instructive to consider the range ofactuator positions and differential pressures for a desired LP-EGR flowrate v₁*. For example, solid line 615 in graph 610 is the subset ofactuator positions corresponding to a desired LP-EGR flow rate v₁*=50kg/h. Solid line 635 graph 630 is the subset of achievable differentialpressures given the constraint of achieving a desired LP-EGR flow ratev₁*=50 kg/h. The minimum LP-EGR differential pressure v₂ ^(min)=12 hPaoccurs when the LP-EGR valve position is u₁=100% and the LP intakethrottle positions is u₂=60%. The maximum LP-EGR differential pressurev₂ ^(max)=56 hPa occurs when the LP intake throttle position is u₂=100%and the LP-EGR valve position is u₁≈12%. Therefore, to minimize thedifferential pressure v₂ while achieving the desired LP-EGR flow ratev₁*, the LP-EGR valve actuator must first saturate and then LP intakethrottle actuator can track the flow rate. In this way, the controllermay function as a chained-actuator controller.

FIG. 7 shows a set of graphs 700 illustrating the LP-EGR controllerfunctioning as a multivariable controller during a Federal TestProcedure (FTP75) drive cycle in accordance with the current disclosure.In particular, the set of graphs 700 show a portion of the FTP75 drivecycle corresponding to the second vehicle-speed “hill” during the hotphase of the drive cycle.

Graph 710 shows a LP-EGR flow rate W_(lpEgr) over time. The dashed linein graph 710 represents the LP-EGR flow rate setpoint W_(lpEgrDes),while the solid line represents the measured LP-EGR flow rateW_(lpEgrMeas). Graph 720 shows a LP-EGR differential pressure Δp_(lpEgr)over time. The dashed line in graph 720 represents the LP-EGRdifferential pressure setpoint Δp_(lpEgrDes), while the solid linerepresents the measured LP-EGR differential pressure Δp_(lpEgrMeas). Thedesired LP-EGR differential pressure Δp_(lpEgrDes)=15 hPa, with theexception of Δp_(lpEgrDes)=0 hPa when the desired LP-EGR flow rateW_(lpEgrDes)=0 kg/h. Graph 730 shows a measured LP intake throttleposition θ_(lpIntThr) over time. The LP intake throttle positionθ_(lpIntThr) is shown as a percentage ranging from 0% to 100%, that is,fully open to fully closed. Graph 740 shows a measured LP-EGR valveposition θ_(lpEgrVlv) over time. The LP-EGR valve position θ_(lpEgrVlv)is shown as a percentage ranging from 0% to 100%, that is, fully closedto fully open.

Graph 710 shows a strong correlation between the measured LP-EGR flowrate and the desired LP-EGR flow rate. The root-mean-square (RMS) LP-EGRflow rate control error is 2.1 kg/h. Graph 720 shows a strongcorrelation between the measured LP-EGR differential pressure and thedesired LP-EGR differential pressure. The measured LP-EGR differentialpressure is unable to achieve the LP-EGR differential pressure setpointwhen the setpoint is zero, though the measured LP-EGR differentialpressure is minimized as both actuators are saturated.

Graphs 730 and 740 illustrate the multivariable control behavior of theLP intake throttle 82 and the LP-EGR valve 39. Graph 730 shows that theLP intake throttle is mostly closed for the majority of the cycle andfully opens when the LP-EGR flow rate and differential pressuresetpoints equal zero. The RMS LP intake throttle position variation is4.4%. Meanwhile, the LP-EGR valve is mostly closed for the majority ofthe cycle and fully closes when the LP-EGR flow rate and differentialpressure setpoints equal zero. The RMS LP-EGR valve position variationis 3.6%. These RMS values for LP-EGR flow rate control error andactuator position variation are only significant in comparison to otherresults, and so will be discussed further herein and with regard to FIG.8.

FIG. 8 shows a set of graphs 800 illustrating the LP-EGR controllerfunctioning as a chained-actuator controller during a Federal TestProcedure (FTP75) drive cycle in accordance with the current disclosure.In particular, the set of graphs 800 show a portion of the FTP75 drivecycle corresponding to the second vehicle-speed “hill” during the hotphase of the drive cycle.

Graph 810 shows a LP-EGR flow rate W_(lpEgr) over time. The dashed linein graph 810 represents a LP-EGR flow rate setpoint W_(lpEgrDes), whilethe solid line represents a measured LP-EGR flow rate W_(lpEgrMeas). TheLP-EGR flow rate setpoint trajectory in graph 810 is identical to theLP-EGR flow rate setpoint trajectory in graph 710 of FIG. 7. Graph 820shows a LP-EGR differential pressure Δp_(lpEgr) over time. The dashedline in graph 820 represents a LP-EGR differential pressure setpointΔp_(lpEgrDes) while the solid line represents a measured LP-EGRdifferential pressure Δp_(lpEgrMeas). The desired LP-EGR differentialpressure Δp_(lpEgrDes)=0 hPa throughout the cycle. Graph 830 shows ameasured LP intake throttle position θ_(lpIntThr) over time. The LPintake throttle position θ_(lpIntThr) is shown as a percentage rangingfrom 0% to 100%, that is, fully open to fully closed. Graph 840 shows ameasured LP-EGR valve position θ_(lpEgrVlv) over time. The LP-EGR valveposition θ_(lpEgrVlv) is shown as a percentage ranging from 0% to 100%,that is, fully closed to fully open.

Graph 810 shows a strong correlation between the measured LP-EGR flowrate and the desired LP-EGR flow rate. The RMS LP-EGR flow rate controlerror is 2.9 kg/h. Graph 820 shows that the measured LP-EGR differentialpressure Δp_(lpEgrMeas) is unable to reach the LP-EGR differentialpressure setpoint Δp_(lpEgrDes)=0, as expected, though the measuredLP-EGR differential pressure is roughly minimized about 5 hPa.

Graphs 830 and 840 illustrate the chained-actuator behavior of theLP-EGR valve 39 and LP intake throttle 82. At least one of the actuatorsis saturated at all times during the cycle. When one actuator saturates,the unsaturated actuator is responsible for tracking the LP-EGR flowrate to the setpoint. Consequently, the RMS LP-EGR valve positionvariation is 5.7% and the RMS LP intake throttle position variation is4.7%. That is, there is increased actuator variation compared to themultivariable controller results shown in FIG. 7. The increased actuatorvariation for the chained-actuator control follows physical intuition.Given lower LP-EGR differential pressures, the LP-EGR valve requireslarger magnitude movements to affect equivalent flow rate changes.

The chained-actuator controller minimizes the LP-EGR differentialpressure Δp_(lpEgr) at the expense of a higher LP-EGR flow rateW_(lpEgr) control error and increased actuator variation compared to themultivariable controller.

In the preferred embodiment, the LP-EGR differential pressure setpointis used as a minimum floor value. That is, the LP-EGR differentialpressure setpoint Δp_(lpEgrDes) can be set to a very low value, forexample Δp_(lpEgrDes)=5 hPa, in order to avoid the reduced robustness inthe immediate neighborhood of the singularity at Δp_(lpEgr)=0 hPa in theinverse plant model. In this manner, if the differential pressure isbelow 5 hPa, then the controller will behave as the multivariablecontroller and maintain the differential pressure at 5 hPa whiletracking the LP-EGR flow rate setpoint. However, if the differentialpressure is above 5 hPa, then the controller will operate as thechained-actuator controller, which minimizes the differential pressurenecessary to achieve the LP-EGR flow rate, and correspondingly minimizesthe marginal fuel consumption due to the LP-EGR pumping work.

Note that the example control and estimation routines included hereincan be used with various engines and/or vehicle system configurations.The control methods and routines disclosed herein may be stored asexecutable instructions in non-transitory memory. The specific routinesdescribed herein may represent one or more of any number of processingstrategies such as event-driven, interrupt-driven, multi-tasking,multi-threading, and the like. As such, various actions, operations,and/or functions illustrated may be performed in the sequenceillustrated, in parallel, or in some cases omitted. Likewise, the orderof processing is not necessarily required to achieve the features andadvantages of the example embodiments described herein, but is providedfor ease of illustration and description. One or more of the illustratedactions, operations and/or functions may be repeatedly performeddepending on the particular strategy being used. Further, the describedactions, operations and/or functions may graphically represent code tobe programmed into non-transitory memory of the computer readablestorage medium in the engine control system.

It will be appreciated that the configurations and routines disclosedherein are exemplary in nature, and that these specific embodiments arenot to be considered in a limiting sense, because numerous variationsare possible. For example, the above technology can be applied to V-6,I-4, I-6, V-12, opposed 4, and other engine types. The subject matter ofthe present disclosure includes all novel and non-obvious combinationsand sub-combinations of the various systems and configurations, andother features, functions, and/or properties disclosed herein.

The following claims particularly point out certain combinations andsub-combinations regarded as novel and non-obvious. These claims mayrefer to “an” element or “a first” element or the equivalent thereof.Such claims should be understood to include incorporation of one or moresuch elements, neither requiring nor excluding two or more suchelements. Other combinations and sub-combinations of the disclosedfeatures, functions, elements, and/or properties may be claimed throughamendment of the present claims or through presentation of new claims inthis or a related application. Such claims, whether broader, narrower,equal, or different in scope to the original claims, also are regardedas included within the subject matter of the present disclosure.

1. A turbocharged engine method, comprising: responsive to adifferential between intake and exhaust pressure below a threshold,adjusting a LP-EGR valve while adjusting a LP intake throttle toregulate a LP-EGR flow rate and the differential to respectivesetpoints; and responsive to the differential above the threshold,saturating the LP-EGR valve to minimize the differential while actuatingthe throttle to regulate the flow rate to its setpoint.
 2. The method ofclaim 1, wherein regulating the LP-EGR flow rate to the flow ratesetpoint is prioritized over regulating the differential to thedifferential setpoint.
 3. The method of claim 1, wherein the thresholdis 5 hectopascals.
 4. The method of claim 1, wherein the flow ratesetpoint is based upon engine operating conditions.
 5. The method ofclaim 1, wherein the differential setpoint is equivalent to thethreshold.
 6. The method of claim 1, using a pair ofproportional-integral controllers and a linearization controller tocontrol the LP intake throttle and the LP-EGR valve.
 7. The method ofclaim 6, wherein the linearization controller is based on aphysics-based model of the LP-EGR system, the physics-based model basedon assumptions of an incompressible exhaust gas and a steady-statedynamics of the LP-EGR valve and the LP intake throttle.
 8. The methodof claim 1, wherein the turbocharged engine includes an EGR passage, andthe EGR passage couples an engine exhaust, downstream of a turbine, toan engine intake, upstream of a compressor.
 9. The method of claim 8,wherein the LP-EGR valve is positioned in the EGR passage upstream ofthe compressor, and wherein the LP intake throttle is positioned in anair intake passage of the engine intake upstream of the compressor. 10.The method of claim 1, wherein the flow rate is measured downstream ofthe LP-EGR valve.
 11. A turbocharged engine method, comprising:responsive to a differential between intake and exhaust pressure below athreshold, adjusting a LP-EGR valve while adjusting a LP intake throttleto regulate a LP-EGR flow rate and the differential respectively to aflow setpoint and a differential setpoint; and responsive to thedifferential above the threshold, in a first mode saturating the LP-EGRvalve to minimize the differential while actuating the throttle toregulate the flow rate to the flow setpoint, and in a second mode,saturating the intake throttle to minimize the differential whileactuating the LP-EGR valve to regulate the flow rate to the flowsetpoint.
 12. The method of claim 11, wherein regulating the LP-EGR flowrate to the flow setpoint is prioritized over regulating thedifferential to the differential setpoint.
 13. The method of claim 11,wherein the flow rate is measured downstream of the EGR valve.
 14. Themethod of claim 11, wherein the differential setpoint is equivalent tothe threshold.
 15. The method of claim 11, wherein the threshold is 5hectopascals.
 16. The method of claim 11, wherein the flow setpoint isbased upon an engine operating condition.
 17. The method of claim 11,using a pair of proportional-integral controllers and a linearizationcontroller to control the LP intake throttle and the LP-EGR valve. 18.The method of claim 17, wherein the linearization controller is based ona physics-based model of the LP-EGR system, the physics-based modelbased on assumptions of an incompressible exhaust gas and a steady-statedynamics of the EGR valve and the LP intake throttle.
 19. An internalcombustion engine system comprising: a turbocharger including acompressor connected to a turbine, the compressor in communication withan intake manifold of the engine and the turbine in communication withan exhaust manifold of the engine; a low-pressure (LP) exhaust gasrecirculation (EGR) passage including an EGR valve and an intakethrottle connecting the intake manifold and the exhaust manifold, saidEGR valve responsive to an EGR valve control signal and said intakethrottle responsive to an intake throttle control signal for regulatinga flow rate into said intake manifold and a differential pressure insaid LP-EGR passage; a controller configured with instructions stored innon-transitory memory that when executed, cause the controller to:generate a flow rate error based upon a reference flow rate and ameasured flow rate; generate a differential pressure error based upon areference differential pressure and a measured differential pressure;calculate a minimum and a maximum achievable flow rates; apply theminimum and the maximum achievable flow rates as anti-windup limits to afirst proportional-integral controller; execute the firstproportional-integral controller to generate an adjusted flow ratesetpoint responsive to the flow rate error; calculate a minimum and amaximum achievable differential pressures responsive to the adjustedflow rate setpoint; apply the minimum and the maximum achievabledifferential pressures as anti-windup limits to a secondproportional-integral controller; execute the secondproportional-integral controller to generate an adjusted differentialpressure setpoint responsive to the differential pressure error; executea linearization controller to generate an EGR valve actuator positionand a LP intake throttle actuator position responsive to the adjustedflow rate setpoint and the adjusted differential pressure setpoint; andactuate the EGR valve to the EGR valve actuator position and the LPintake throttle to the LP intake throttle actuator position.
 20. Thesystem of claim 19, wherein the linearization controller is based on aphysics-based model of the LP-EGR system, the physics-based model basedon assumptions of an incompressible exhaust gas and a steady-statedynamics of the EGR valve actuator and the LP intake throttle actuator.